Check the pressure; when, just turning it over and it should maintain that pressure (check the manual for spec and how long it should maintain the pressure) when the key is turned off. When my fuel pump went out; it was not maintaining pressure, when the car was off.... went to zero but in my case, the pressure was ok when running! I think, my pump was in the process of dying; it was getting progressively harder and harder to start, as the pressure was not up to spec. I can only assume; eventually, it would not have stated at all.
My 02 1.8t just did this, this past November. Pain in the butt trying to diagnose it.
When you open the drivers door do you hear the pump prime? It should also prime then the key is turned. If not it could very well be the pump or the relay! Mine turned out to be the pump after replacing the relay, and re-replacing the relay with the old one!